Simple familly computer advice needed - intel vs AMD

Hi all
I need to replace my parents computer as its randomly freezing (even during a windows install) and I cant seem to find the root cause (although it may well be the motherboard).
The machine will be used mostly for office, internet and a very amateur amount of photo manipulation, so does not need to be special in any way as no 3d games will be run (freecell at the most!)
What it does need to be is 100% stable and rock solid so I don’t get any grief

I have found two potential barebones systems which will be by far the simplest solution and here is where I would appreciate some advice on to go intel or AMD.

Thank for all of your help, in a shock move the parents decided to pay more for the system so I took all your advice and went core 2 duo.
Barebones Bundles - Heatsink and Fan, 1GB DDR2 800Ram, Intel Core 2 Duo E6550 Intel G33 Motherboard